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How do you find the derivative of ${4^{6x}}$?

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Last updated date: 18th Jun 2024
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Answer
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Hint: Differentiation is one of the two important concepts apart from integration. Differentiation is a method of finding the derivative of a function. Differentiation is a process, in Maths, where we find the instantaneous rate of change in function based on one of its variables. The most common example is the rate change of displacement with respect to time, called velocity. The opposite of finding a derivative is anti-differentiation.
If x is a variable and y is another variable, then the rate of change of x with respect to y is given by $\dfrac{{dy}}{{dx}}$. This is the general expression of derivative of a function and is represented as $f(x) = \dfrac{{dy}}{{dx}}$, where$y = f(x)$ is any function.

Complete step by step answer:
We can rewrite ${4^{6x}}$as ${({4^6})^x}$
Now, recall $\dfrac{d}{{dx}}{a^x}$ where a is a constant is given by ${a^x}ln(a)$.
Thus,
$ \Rightarrow \dfrac{d}{{dx}}{4^{6x}} = {4^{(6x)}}ln({4^6}) = 6ln(4){4^{(6x)}}$

Note: Functions are usually categorized under calculus in two categories, namely:
1) Linear functions.
2) Non-linear functions.
A linear function varies by its domain at a constant rate. Therefore, the overall rate of feature shift is the same as the level of function change in any situation.
Nevertheless, in the case of non-linear processes, the rate of change ranges from point to point. The variation's existence is dependent on the function's design.
The frequency of function change at a given point is known as a derivative of that function.